【精品】hypothesistesting（可编辑.ppt

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1、HypothesisTesting假设检验假设检验2Population:The UniverseData or information that defines the entire setParameters(m,s)may,or may not be known.Sample:A subset data or information that possesses the same characteristics as that of the population.We can calculate statistics(X Bar,s).We make decisions about th

2、e population based on the sampleWe make decisions about the population based on the sampleHow many samples should be How many samples should be taken?taken?Why should we take a Why should we take a sample?sample?Should the sample be random?Should the sample be random?Is it possible to have Is it pos

3、sible to have sampling error?sampling error?Populations and Samples5样本样本?为何使用样本为何使用样本?n为何采用样本而非总体?n采用样本可减少时间和成本消耗n即使可能，获取总体数据也是非常困难的.n何时采用样本？n我们利用样本定流程基线n利用样本对过程的可控变化结果进行评估.n如何获取样本?n请看第五部分.8Sample AAll processes have variation.Samples from a given process may vary.Sample BHow can we differentiate be

4、tween sample based“chance”variation and a true process difference?How can we depend on a sample?9样本样本 A所有的过程都有差异.来源于给定过程的样本也可能是多样化的.样本样本 B我们怎样区分随机变化的样本和真实总体的差别呢?怎样使用样本？怎样使用样本？10Confidence Intervals and Point EstimatesnConfidence intervals identify a range of plausible values for a sample statistic o

5、f a population parameter.They can be either one-sided or two-sided.Sample Means,Sample Standard deviation,Sample Variances and other sample statistics are known as Point Estimators because they are single values used to represent population parameters11可信区间和特征值的估计可信区间和特征值的估计n可信区间可信区间 确定了总体参数中样确定了总体参

6、数中样本统计可能的数值范围本统计可能的数值范围.它它们们可以是单边也可是双边可以是单边也可是双边。样本均值、样本标准偏差、样本方样本均值、样本标准偏差、样本方异和其它样本统计被称为特征值评异和其它样本统计被称为特征值评估者。因为它们是用以代表总体参估者。因为它们是用以代表总体参数的单一数的单一数数值。值。12Hypothesis TestsnPoint Estimates of parameters and Confidence Interval Interpretation are both means for making inferences about sample data.nHyp

7、othesis tests are designed to help us make an inference about the true population value at the desired level of confidence.nWe will use confidence intervals and tests of sample means,variances and sample standard deviation to investigate difference and cause/effect relationships using data.Hypothesi

8、s Tests help determine if an apparent difference is real or could be due to chance.By using data and hypothesis testing,we can quantify our level of confidence that the difference is real.13假设检验假设检验n对参数特征值估计和可信区间的诠释都是得出样本数据推论的路径.n假设检验是用以帮助我们在需要的可信度上对真实的总体数值进行推论的。n我们将用可信区间和样本均值、样本差异及样本标准偏差测验来研究使用数据的差

9、別和因果关系。假设检验有助于判断一个明显的差别是否真实存在还是偶然的，假设检验有助于判断一个明显的差别是否真实存在还是偶然的，而且还可以提高差异真实性的可信度而且还可以提高差异真实性的可信度.14A Statistical HypothesisAn assertion or conjecture about one or more parameters of the populationTo determine whether it is true or false,we must examine the entire population.This is impossible!Instead

10、 use a random sample to provide evidence that either supports or does not support the hypothesis.The conclusion is then based upon statistical significance.It is important to remember that this conclusion is an inference about the population determined from the sample data.15统计假设统计假设对对于一个或多个总体于一个或多个

11、总体里里的参数的肯定或推断的参数的肯定或推断为了判断它的正误，我们必须检查总体的全部。这是不可能的！为了判断它的正误，我们必须检查总体的全部。这是不可能的！我们应使用随机样本，观察其是否能支持该假设我们应使用随机样本，观察其是否能支持该假设.从而该结论是建立在统计学意义的基础之上的从而该结论是建立在统计学意义的基础之上的.必须记住该有关总体的结论是由样本推测出的必须记住该有关总体的结论是由样本推测出的.16Why Do Hypothesis Testing?1.To improve processes,we need to identify factors which impact the m

12、ean or standard deviation.2.Once we have identified these factors and made adjustments for improvement,we need to validate actual improvements in our processes.3.Sometimes we cannot decide graphically or by using calculated statistics(sample mean and standard deviation)if there is a statistically si

13、gnificant difference between processes.4.In such cases the decision will be subjective.5.We perform a formal statistical hypothesis test to decide objectively whether there is a difference.Data helps everyone makes the same decisionData helps everyone makes the same decision.17为何要做假设检验为何要做假设检验?1.为了改

14、进过程，我们需要确定影响均值和标准偏差的因素为了改进过程，我们需要确定影响均值和标准偏差的因素.2.一旦确定了这些因素并对改进措施进行了调整，我们就需一旦确定了这些因素并对改进措施进行了调整，我们就需要验证其在过程中的切实效果。要验证其在过程中的切实效果。3.若过程中存在统计上的重大差别，有时我们就不能利用图若过程中存在统计上的重大差别，有时我们就不能利用图表或算得的统计数据（样本均值和样本标准偏差）作出决表或算得的统计数据（样本均值和样本标准偏差）作出决策策.4.在这种情况下，决定可能是主观的在这种情况下，决定可能是主观的.5.我们采用我们采用正统正统假设检验以客观地判断是否存在差別。假设检

15、验以客观地判断是否存在差別。数据帮助数据帮助每个每个人作出同样的决定。人作出同样的决定。18Nature of HypothesesnNull Hypothesis(Ho):nUsually describes a status quonThe one you assume unless otherwise shownnSigns used in Minitab:=nAlternative Hypothesis(Ha):nUsually describes a differencenThe one you accept or reject based upon evidencenSigns u

16、sed in Minitab:not=or OrOr Its either Null(same)or Alternative(Different)19假设的种类假设的种类n虚无性假设n通常用以描述现状n除非其它方面有所说明，否则就是人为设想的。n在Minitab中用“=”表示n选择性假设(Ha):n通常用以描述差別n以证据为基础接受或拒绝的类型n在Minitab中用“not=or”表示OrOr 不是不是全全虚虚性性假设（相同）就是选择性假设（相区别的）假设（相同）就是选择性假设（相区别的）20Hypothesis TestingGuilty vs.Innocent ExampleThe Ame

17、rican justice system can be used to illustrate the concept of hypothesis testing.In America we assume innocence until proven guilty.Innocence corresponds to the null hypothesis.It requires strong evidence,“beyond a reasonable doubt,”to convict the defendant.Returning a guilty verdict corresponds to

18、rejecting the null hypothesis and accepting the alternative hypothesis.More specifically,we have significant evidence to support that a difference exists.Ho:Person is innocent.Ha:Person is guilty.What are the possible outcomes when the truth is known?21假设检验假设检验有罪有罪 vs.无罪的案例无罪的案例美国的司法体系可以用于阐述假设检验的概念.

19、在美国罪犯在被判有罪之前均是清白的.清白对应虚无性假设.它需要强而有力的证据，必需“排除所有合理的怀疑”才能把被告定罪.若陪审团裁定被告有罪则相当于拒绝虚无性假设接受选择性假设.更具体些更具体些,我们拥有重要的证据证明差別的存在我们拥有重要的证据证明差別的存在.Ho:被告是清白的被告是清白的.Ha:被告有罪被告有罪.当得知真相后，可能的结果是什么当得知真相后，可能的结果是什么?22TruthVerdictHo,=Ha,not=Ho,=Ha,not=InnocentJailedGuilty Set FreeInnocentSet FreeGuiltyJailedSet FreeJailInnoc

20、entGuiltyThe Type I Error(error)is rejecting Ho when it is true sometimes called the producers risk.The Type II Error(error)is failing to reject Ho when it is false sometimes called the consumers risk.DecisionType 1Error Type 2Error CorrectDecisionCorrectDecisionTruthHo,=Ha,not=Ho,=Ha,not=Risk Decis

21、ion Making in our Courts and in Business23真相真相裁决裁决Ho,=Ha,not=Ho,=Ha,not=清白清白监禁监禁有罪有罪释放释放清白清白释放释放有罪有罪监禁监禁释放释放监禁监禁清白清白有罪有罪Type I 错误错误(错误错误)当当 Ho 是是无无误时而误时而拒绝拒绝 有时称作有时称作 生产者风险生产者风险Type II 错误错误(错误错误)是当是当 Ho有错误时却有错误时却接受接受 有时称作有时称作 消费者风险消费者风险.DecisionType 1错误错误 Type 2错误错误 正确正确决定决定正确正确决定决定真相真相Ho,=Ha,not=Ho

22、,=Ha,not=法庭和商业上的决策风险法庭和商业上的决策风险24The p ValuenAnother way to measure the risk in the decision is through the p Value.nThe p-value is known as the Observed Level of Significance for a factor.nIt is the chance of observing this amount of difference if the sample is consistent with the population.nThe p

23、-value is also the probability of being wrong if we reject the Null Hypothesis(Type I Error.)nUnless there is an exception based on engineering judgment,we will set an acceptance level of a Type I error at a=0.05.nThus,any p-value less than 0.05 means we reject the Null hypothesis.25p 值值n衡量决策风险的另一种方

24、法是通过衡量决策风险的另一种方法是通过P值值.nP值是指一个因素可测的重要性水平.n当样本和总体相对时，P值是指观测到其中差別的机会率.nP值也指如果拒绝虚无性假设可能发生错误的概率（错误I）n除非在基于工程判断上的例外，我们将错误I 的可接受水平定在a=0.05.n从而，任何小于0.05的P值就表示虚无性假设被拒绝。26Defining HypothesesNull HypothesesHO:X1=TargetHO:X1=mHO:X1-X2=0HO:m1-m2=0HO:X1=X2=X3=.XnHO:s1=s2HO:S1=S2HO:S1=S2=S3=.SnAlternative Hypothe

25、sesHA:m1m2 Inequalities are two sided testsHA:X1X2HA:m1m2HA:X1X2 One Sided test are used for hypotheses.HA:m1m2HA:X1X2HA:X1-X20 _HA:X1-X20 _HA:s1s2 _HA:s1S2 _Scripting Hypotheses as equations is useful when stating.27定义假设定义假设虚无性假设HO:X1=TargetHO:X1=mHO:X1-X2=0HO:m1-m2=0HO:X1=X2=X3=.XnHO:s1=s2HO:S1=S2

26、HO:S1=S2=S3=.Sn选择性假设HA:m1m2 不等式是针对两边的测试HA:X1X2HA:m1m2HA:X1X2 单边测试用于 假设.HA:m1m2HA:X1X2HA:X1-X20 _HA:X1-X20 _HA:s1s2 _HA:s1S2 _把假设以等式陈述很有用把假设以等式陈述很有用.28Hypothesis Testing ProtocolThe hypotheses are always statements about the population parameters.1.State your null hypothesis(Ho)HO:The height of citiz

27、ens in country A is equal to the height of citizens in country B(m A=m B).State your Alternative Hypothesis(Ha)HA:The height of citizens in country A is less than the height of citizens in country B(m A m B).2.Determine the appropriate statistical test based on the Hypothesis being tested.3.Determin

28、e the level of acceptable risk.a Risk:usually 5%(Default)b Risk:Usually 10 20%(Default)29假设检验协议假设检验协议假设总是关于总体参数的假设总是关于总体参数的陈述陈述.1.定明虚无性假设(Ho)HO:A国与B国居民身高相等(m A=m B).规定选择性假设(Ha)HA:A国居民身高低于B国居民的身高(m A m B).2.基于在需被测试的假设上，决定适合的统计测试.3.决定可接受的风险程度.a 风险:通常 5%(预设值)b 风险:通常10 20%(预设值)30Hypothesis Testing Proto

29、col(Cont)4.Determine the proper sample size for the test(Section 5)5.Collect a sample of observations from the population.6.Calculate statistics based on the sample.7.Use a statistical test to test alternative hypothesis.8.Based on the test result,we accept or reject Ho based on the previously deter

30、mined criterion.9.Translate the results.Translate the statistical conclusion to a practical one.Statistical Conclusion:Can we prove difference statistically.Practical Conclusion:Do we care about the difference?31假设检验协议假设检验协议(续续)4.决定适合测试的样本数量(第五部分)5.从总体中选取需观察的样本群.6.计算样本的统计.7.用统计测试方法测验选择性假设.8.在测试结果的基础

31、上，根据先前确定的标准，做出选择或拒绝Ho 的决定.9.转化结果.将统计的结论转换为现实的结果.统计结论:我们能从统计的角度证明差別吗？现实结果:我们需注意这些差別吗?32Well be using hypothesis testing as a method to prove changeTarget or Target or desired desired valuevalueOne Sample tOne Sample tAre multiple Are multiple samples the samesamples the sameMean:two sample t or Mean:

32、two sample t or ANOVAANOVAVariation:F test or Test for Variation:F test or Test for Equal VarianceEqual VarianceProportion of OccurrenceProportion of Occurrence:Chi Square Chi Square C C C C2 2 33我们将假设检验作为证明差异的一种我们将假设检验作为证明差异的一种方法方法目标目标目标目标数数值值值值一个样本一个样本一个样本一个样本 t t若干样本是否一致若干样本是否一致若干样本是否一致若干样本是否一致一致一致一致一致:两个两个两个两个 t t样本样本样本样本 或或或或ANOVAANOVA不一致不一致不一致不一致:用用用用F F测试测试测试测试 或均等或均等或均等或均等差异差异差异差异测测测测试试试试 事情发生的概率事情发生的概率事情发生的概率事情发生的概率:Chi Square Chi Square C C C C2 2 34